# Faithful extension on finite order classes

@article{Guillet2017FaithfulEO, title={Faithful extension on finite order classes}, author={Alain Guillet and Jimmy Leblet and Jean-Xavier Rampon}, journal={Australas. J Comb.}, year={2017}, volume={69}, pages={1-17} }

In the particular case of finite orders, we investigate the notion of faithful extension among relations introduced in 1971 by R. Fräıssé: an order Q admits a faithful extension relative to an order P if P does not embed into Q and there exists a strict extension of Q into which P still does not embed. For most of the known order classes, we prove that if P and Q belong to a class then Q admits a faithful extension in this class. For the class of distributive lattices, we give an infinite… Expand

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#### References

SHOWING 1-10 OF 20 REFERENCES

Chain Dominated Orders

- Mathematics, Computer Science
- Order
- 2006

Finite partial orders which have a chain such that every element of the order either belongs to this chain or has all its covers in this chain are shown to be exactly the orders being both interval orders and truncated lattices. Expand

An Introduction to Lattices and Order

- Mathematics, Computer Science
- 1989

This chapter discusses the structure of finite distributive lattices and finite Boolean algebras, and the role of lattices in algebra in this structure. Expand

Ordered Sets: An Introduction

- Mathematics
- 2012

Preface * List of Figures * The Basics * Chains, Antichains and Fences * Upper and Lower Bounds * Retractions * Lattices * Truncated Lattices * The Dimension of Ordered Sets * Interval Orders *… Expand

Combinatorics and Partially Ordered Sets: Dimension Theory

- Mathematics
- 1992

Primarily intended for research mathematicians and computer scientists, Combinatorics and Partially Ordered Sets: Dimension Theory also serves as a useful text for advanced students in either field.… Expand

L'extension respectueuse à hauteur constante entre posets finis

- Mathematics
- 1993

Le probleme d'extension respectueuse est trivial dans le cas general d'une relation binaire ou pour la classe des posets finis (poset=ensemble partiellement ordonne). Cependant il devient interessant… Expand

Sur la comparaison des types de relation

- C.R. Acad. Sci. Paris, t. 226 (1948), 987–988. A. GUILLET ET AL. /AUSTRALAS. J. COMBIN. 69 (1)
- 2017

Abritement entre relations et spécialement entre châınes

- Mathematica, Vol. V (INDAM, Rome, 1969/70)
- 1971

Lattice theory

- American Mathematical Society Colloquium Publications Volume XXV
- 1967